论文标题
带有模态运算符的分布完整的Lambek演算
The Distributive Full Lambek Calculus with Modal Operators
论文作者
论文摘要
在本文中，我们研究了有界分配残留的晶格的逻辑，并考虑了在非交通设置中考虑$ \ box $和$ \ diamond $的模态操作员。我们介绍了这种子结构模态逻辑的关系语义。我们证明，任何规范逻辑都是通过离散二元性和规范扩展完成的Kripke。也就是说，我们表明，如果在规范扩展下关闭其品种，则分布式完整Lambek演算的模态扩展是其帧的逻辑。之后，我们建立了基于普里斯特利空间的残留分配模态代数和拓扑kripke结构之间建立祭司风格的二元性。
In this paper, we study logics of bounded distributive residuated lattices with modal operators considering $\Box$ and $\Diamond$ in a noncommutative setting. We introduce relational semantics for such substructural modal logics. We prove that any canonical logic is Kripke complete via discrete duality and canonical extensions. That is, we show that a modal extension of the distributive full Lambek calculus is the logic of its frames if its variety is closed under canonical extensions. After that, we establish a Priestley-style duality between residuated distributive modal algebras and topological Kripke structures based on Priestley spaces.
